When you ride a bicycle at constant speed, almost all of the energy you expend g

Question

When you ride a bicycle at constant speed, almost all of the energy you expend goes into the work you do against the drag force of the air. In this problem, assume that all of the energy expended goes into working against drag. The drag force on an object is approximately proportional to the square of its speed with respect to the air. For this problem, assume that F~V^2 exactly and that the air is motionless with respect to the ground unless noted otherwise. Suppose a cyclist and her bicycle have a combined mass of 60kg and she is cycling along at a speed of 5 m/s .

A.)If the drag force on the cyclist is 20N , how much energy does she use in cycling 1Km ?

B.)Under these conditions, how much power does she expend as she cycles?

C.)If she doubles her speed to 10m/s , how much energy does she use in cycling 1 kilometer?

D.)How much power does she expend when cycling at that speed? (10m/s)

E.)Upon reducing her speed back down to 5m/s , she hits a headwind of 5m/s . How much power is she expending now?
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Explanation / Answer

Work done = force * distance A. She cycles 1000 m against a force of 10 N {1km = 1000 m} Work done = energy expended = 10 * 1000 = 10000 J B. Power = energy / time. So we need to know how long it takes her to cycle 1000m Speed = distance / time so time = distance / speed = 1000 m / 5 m/s = 200 s Power = 10000 / 200 = 50 W C. "Assume that F is proportional to v^2 exactly" so if she doubles her speed the drag force will be 4 times as much = 4 * 10 N = 40 N Work done = energy expended = 40 * 1000 = 40000 J D. At 10 m/s it will only take her 100 s to cycle 1000m Power = 40000 / 100 = 400 W E. Her speed relative to the air is 5 +5 = 10 m/s so the drag force is still 40 N. Now though she is only moving along the road at 5 m/s, so it will take her 200 s to complete the 1000 m distance. Work done = energy expended = 40 * 1000 = 40000 J Power = 40000 / 200 = 200 W

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